Cutting + crossfading produces no silent parts except the viable information of the event is far from the previous/next event. Try it this way: cut the part you want to move left and right, hold ctrl+alt and drag it. There will be no gaps between the events, instead the content of the event you drag is sliding through that cut piece.
Group editing was introduced in Cubase 6 I think. In former Cubase versions you can group events though (i.e. all drum tracks) and use the same slide through method. Of course you can also move the grouped events and fill the gaps with crossfades. Both methods do the same actually.